It takes an Act of Congress to create or abolish a department or agency, or to transfer responsibility from one department to another. Note that from time to time Congress had granted the President authority to enact reorganization plans to move or consolidate functions from one agency to another, but it has been decades since the Congress has let the President do so. Mainly that is because of INS v. Chadha which in 1983 found the legislative veto to be unconstitutional, and the reorganization authority which had been granted made use of it. Congress has generally been unwilling to give the executive branch carte blache to reorganize itself.

It may be better to rely on legislation, than the British habit of the Prime Minister renaming and rearranging departments during cabinet reshuffles. It sometimes seems changes are just made to meet some immediate (and probably transient) political need, with no real thought to the long term administrative logic of the new arrangements. There is something to be said for the greater difficulty in making changes found in the US system.

The reason why changes can be made so easily in the UK system is that most, non financial, areas of government, are entrusted to the Secretary of State. This is, in theory, a single office with multiple holders. Although it has been customary, for several centuries, to assign particular functions to individual Secretaries of State these can be reallocated with no great formality.

Typically legislation on Ministers of the Crown prescribes the maximum number of paid ministers of a particular kind, but not the particular function of each.